NuHAG :: TALKS

Talks given at NuHAG events

Gabor expansions of signals: Computational aspects and open questions


  Hans G. Feichtinger

  given at  atfa2017 (06.06.17 10:20)
  id:  3299
  length:  45minmin
  status:  accepted
  type:  talk
  LINK-Presentation:  https://nuhagphp.univie.ac.at/dateien/talks/3299_ATFA17A.pdf
  ABSTRACT:
Although the theory of Gabor Analysis, i.e. the decomposition of distributions over locally compact groups in terms of TF-shifted copies of a Gabor atom along a lattice is theoretically well understood there are still many interesting open questions concerning the practical realization of such a program.

Aside from the classical case, where one-dimensional signals on the real line are expanded, using a separable TF-lattice of the form $aZxbZ$ there is no easily applicable and computationally realizable approach to the actual determination of Gabor coefficients for more general lattices, or for multi-dimensional signals.

The talk will address computational issues, the theoretical justification of numerical approximations to the continuous problem, and mention a list of open problems in the field which would be relevant for further progress and real-world applications of Gabor analysis. We will also discuss aspects of the question, what makes a Gabor frame a good one.


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